Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=12.

Question

y=7 when x=3
Write a direct variation equation that relates x and y.

Answer 1

The direct variation equation relating x and y can be written as y = kx, where k is the constant of variation.

To find the value of k, we can use the given information that y = 7 when x = 3. Plugging these values into the direct variation equation yields:

7 = k(3)

To solve for k, we divide both sides of the equation by 3:

7/3 = k.

So, the value of k is 7/3.

Thus, the direct variation equation relating x and y is y = (7/3)x.

To find the value of y when x = 12, we substitute x = 12 into the equation:

y = (7/3)(12)
y = 84/3
y = 28.

Therefore, when x = 12, y = 28.